Answer: 1
Step-by-step explanation:
In order to find GCF, take the prime factorization of 3 and 13.
3: 1*3 ==> Prime factorization of 3
13: 1*13 ==> Prime factorization of 3
The common factor is 1.
GCF of 13 and 3 is 1
0.000000006450 in scientific notation
Answer:
[tex]6.45*10^{-9}[/tex]
Step-by-step explanation:
Please help me with this problem im confused.
Answer: A. D.
Step-by-step explanation:
A.
x-b-3<0
x-b-3+3<0+3
x-b<3 (yes)
B.
0>b-x+3
0+x>b-x+3+x
x>b+3
x-b>b+3-b
x-b>3 (no)
C.
x<3-b
x+b<3-b+b
x+b<3 (no)
D.
-3<b-x
-3+3<b-x+3
0<b-x+3
0+x<b-x+3+x
x<b+3
x-b<b+3-b
x-b<3 (yes)
Answer:
A and D
Step-by-step explanation:
Option A
[tex]\begin{aligned}& \textsf{Given inequality}: & x-b-3 & < 0\\& \textsf{Add 3 to both side}: \quad & x-b-3+3 & < 0+3\\& \textsf{Simplify}: & x-b & < 3\end{aligned}[/tex]
Option B
[tex]\begin{aligned}& \textsf{Given inequality}: & 0 & > b-x+3\\& \textsf{Add $x$ to both sides}: & 0+x & > b-x+3+x\\& \textsf{Simplify}: & x & > b+3\\& \textsf{Subtract $b$ from both sides}: \quad& x-b & > b+3-b\\& \textsf{Simplify}: & x-b & > 3\end{aligned}[/tex]
Option C
[tex]\begin{aligned}& \textsf{Given inequality}: & x & < 3-b\\& \textsf{Add b to both sides}: \quad & x+b & < 3-b+b\\& \textsf{Simplify}: & x+b & < 3\end{aligned}[/tex]
Option D
[tex]\begin{aligned}& \textsf{Given inequality}: & -3 & < b - x\\& \textsf{Divide both sides by -1}: \quad & \dfrac{-3}{-1} & > \dfrac{b}{-1}-\dfrac{x}{-1}\\& \textsf{Simplify}: & 3 & > -b+x\\& \textsf{Simplify}: & x-b & < 3\end{aligned}[/tex]
Note: When multiplying or dividing by a negative number in an inequality, remember to flip the inequality sign.
18 Shifting the origin to another point (h,k) without Changing the directions of the axes. If P(x,y) with reference to original axes changes to P(X,Y) with reference new axes then i) x=X-h, y=Y-k ii) x=X-h,y=Y+k iii) x= x+h, y=Y+k iv)x=x-y=Y-k
If we shift the origin without changing the direction and point P(x, y) is changed to P(X, Y) then the new coordinates will be x = X + h and y = Y + k.
Shifting of origin is the phenomenon of changing the coordinates of the origin which is generally (0, 0) to another point which has coordinated (h, k). This phenomenon is usually carried out graphically. This is done when there is difficulty to solve the problems in coordinate geometry when we take the origin at (0, 0).
If we shift the origin which is at P(x, y) to another point (h, k) then the coordinates of new point P(X, Y) will be
x = X + h and y = Y + k
If h is positive, then coordinates will be x = X + h and if h is negative then coordinates will be x = X - h. If k is positive, then coordinates will be y = Y + k and if k is negative then coordinates will be y = Y - k.
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jean gray earns a graduated commission of 4 on her first $2000 of sales and 8 on all sales over $2000 jean's sales for the past week totaled $3925
Her commission for the week was $234.
It is given the total earning in past week = $3,925 and jean earns 4% for the first $2000
So, the commission = $2000 x 4/100 = $80
To find additional sales, the formula to refer is
Add –on sales = total sales – base sales
= 3,925 – 2000
= 1,925
For the $1,925 sales, Jeans earns 8% commission, Her commission
= 1,925*0.08 = $154
So, the total commission = $80 + $154 = $234
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a national survey conducted among a simple random sample of 1,507 adults shows that 56% of americans think the civil war is still relevant to american politics and political life.
a)
[tex]z=4.658\\p_v=P(z > 4.65)=1-P(z < 4.65)=1.581x*10^{-6}[/tex]
b) By assuming a significance level of α = 0.05 and observing that [tex]p_v[/tex] > α, we can reject the null hypothesis at this level of significance. And in this instance, it makes sense that more than 50% of Americans believe that the Civil War still has an impact on American politics and political life.
c) The confidence interval at 90% would be shown (0.527;0.593).
About 54% to 59% of all Americans, in our opinion, believe that the Civil War is still significant today.
What is a survey?A survey is a set of questions used in human subject research with the goal of gathering specific information from a certain population. Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers.
a)
1) The presented data and the notation "n=1507" refer to the random sample of Americans, "X" denoting the proportion of those Americans in the sample who believe that the Civil War is still significant to American politics and political life, and "p cap" denoting the estimated number of those Americans.
Since the problem specifies that majority α=0.05 represents the significance threshold, [tex]p_0[/tex] is the number that we wish to test (no given, but is assumed)
Z would stand for the statistic (interesting variable), and [tex]p_v[/tex] for the p value (variable of interest)
P is the percentage of the public that believes that the Civil War still has an impact on American politics and political life.
2) Useful concepts and formulas
The allegation that more Americans than 50% believe the Civil War is still significant to American politics and political life needs to be tested through a hypothesis (Majority). :
Alternative Hypothesis: p[tex]\geq[/tex] 0.5
Null Hypothesis: p[tex]\leq[/tex] 0.5
The proportion is thought to have a normal distribution.
This test for the percentage of union membership has one tail higher.
Verify whether the sample conforms to the presumptions required for the test to be applied.
a) The random sample must be representative; in this situation, there is no mention of this issue, but it is safe to presume that it exists.
b) The sample size must be sufficient.
[tex]np_0=1507*0.5=753.5 > 10\\n(1-p_0)=1507*(1-0.5)=753.5 > 10[/tex]
3. Determine the statistic.
The formula used to calculate the statistic is as follows:
[tex]z=\frac{p-p_0}{\sqrt{\frac{p_0(1-p_0)}{n} } }= \frac{0.56-0.5}{\sqrt{\frac{0.5(1-0.5)}{1507} } }=4.658[/tex]
P value= [tex]p_v=P(z > 4.65)=1-P(z < 4.65)=1.581*x*10^{-6}[/tex]
According to the alternative hypothesis, the following would be the p value:
P value= [tex]p_v=P(z > 4.65)=1-P(z < 4.65)=1.581*x*10^{-6}[/tex]
Using this formula, the confidence interval would be determined.
p ± [tex]z_{\frac{\alpha }{2}}\sqrt{\frac{p(1-p)}{n} }[/tex]
With the value of [tex]\alpha[/tex] and [tex]\alpha _2[/tex], we can get the quantile necessary for the interval in the normal standard distribution for the 90% confidence interval.
[tex]z_{\frac{\alpha }{2} }=2.58[/tex]
adding the following to the formula for the confidence interval:
[tex]0.56-2.58\sqrt{\frac{0.56(1-0.56)}{1507} } = 0.527\\0.56+2.58\sqrt{\frac{0.56(1-0.56)}{1507} } = 0.593[/tex]
Also provided would be the 90% confidence interval (0.527;0.593).
About 54% to 59% of all Americans, in our opinion, believe that the Civil War is still significant today.
And because the interval does not contain the value of 0.5, we can conclude that, at a 90% level of confidence, the percentage of Americans who believe that the Civil War is still relevant to American politics and political life is higher than 0.5. This result is consistent with the result of part b.
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5-3y+6= 5(y − 1)
How do I solve it with work
AB =
Round your answer to the nearest hundredth.
В
40
C
5
А
The length of the hypotenuse AB is approximately 6.53 units.
In a right angled triangle the side opposite the right angle or the largest side is called the hypotenuse of the triangle.
The length of the hypotenuse is calculated using trigonometric ratios. If in a right-angled triangle, the base angle is θ then:
sin θ = perpendicular ÷ hypotenusecos θ = base ÷ hypotenusetan θ = perpendicular ÷ baseIn the given figure we see in ΔABC
AB is the hypotenuse. ∠BAC = 40 ° AC is the base and BC is the perpendicular.
(The side that contains the given angle is the base and the side opposite the given angle is taken as perpendicular)
Now cos ∠BAC = BC ÷ AB
or, cos 40° = 5 ÷ AB
or, AB = 6.527...
or, AB ≈ 6.53
Hence the value of AB is approximately 6.53 units.
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5x+3 is greater than or equal to x-9
The solution to the mathematical statement 5x+3 is greater than or equal to x-9 is x >= -3
How to determine the inequality solution?The statement is given as:
5x+3 is greater than or equal to x-9
Express as an inequality
5x + 3 >= x - 9
Collect the like terms
5x - x >= -9 - 3
Evaluate the like terms
4x > = -12
Divide both sides by 4
x >= -3
Hence, the solution to the mathematical statement 5x+3 is greater than or equal to x-9 is x >= -3
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Help please (work provided )
Answer:
150 degrees
Step-by-step explanation:
Vertical angles
what is 2.56 - 8.9 =
Answer:
-6.34
Step-by-step explanation:
If you used a number line, it'll help! Start at 2.56, and go back (to the left) 8.9, and you will arrive at -6.34
a circle has a circumference of 615.44615.44615, point, 44 units. what is the radius of the circle? use 3.14 for \piπpi and enter your answer as a decimal.
A circle with a circumference of 615.44 units has a radius of 98 units.
A circle is a round closed figure where all its boundary points are equidistant from a fixed point called the center.
The circumference of a circle is the perimeter of the circle. It is the total length of the boundary of the circle. The circumference of a circle is the product of the constant [tex]\pi[/tex] and the diameter of the circle.
C = [tex]\pi[/tex]D
The diameter (D) is the distance across the circle through the center, it is a line that meets the circumference at both ends and it needs to pass through the center. On the other hand, the radius (r) of a circle is the distance from the center of a circle to any point on the circumference of the circle. Radius is half of the diameter.
If r = 1/2 D, then
D = 2r
Evaluating the value of Din the formula of the circumference,
C = [tex]\pi[/tex](2r)
C = 2[tex]\pi[/tex]r
Using the value of [tex]\pi[/tex] as 3.14 and the circumference as 615.44 units,
evaluate the equation.
C = 2[tex]\pi[/tex]r
615.44 = 2(3.14)r
r = 615.44/ (2*3.14)
r = 98 units
Therefore, the radius of the circle is 98 units.
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Draw this Venn diagram. Classify the following numbers. 45, 24, 52, 30, 66, 15, 85, 90, 72, 60, 20, 38 What can you tell about the numbers in the intersection?
PLEASE HELP I NEED ANSWER PLSS I OFFER 45 POINTS
Answer:
put 244 add 7e8ue
Step-by-step explanation:
i53838 divede 73838
Given that f(x)=x²- 7 and g(x)= 3x + 1, find (fg)(-1/3)
if it exists.
Answer: 7
Step-by-step explanation:
(fg)(-1/3)=
f(g(-1/3))=
f(3(-1/3) + 1)=
f(-1 + 1)=
f(0)=
0²- 7=7
Determine the largest positive interger d such that d+10 is a divisor of d^3+2011
The largest positive integer d for which d +10 is a divisor of d³ + 2011 is equal to 1001.
As given,
Divisor= d +10
Dividend= d³ + 2011
(d³ + 2011 ) ÷ ( d+ 10) = [(d² -10d +100) (d +10) +1011] ÷ ( d+ 10)
=(d² -10d +100) + [ 1011 / (d+10)]
Largest positive integer d for which d +10 is a divisor of d³ + 2011
d + 10 =1011
⇒d=1001
Therefore, the largest positive integer d for which d +10 is a divisor of d³ + 2011 is equal to 1001.
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Twice the sum of a number and 4 is equal to three times the difference of the number and 4. Find the number.
Answer:
The number will be x
Step-by-step explanation:
2(x + 4) = 3(x - 2)
2x + 8 = 3x - 6
14 = x
find the total profit or loss for each color of T-shirt
answer:
Green t-shirt=profit of $1
White t-shirt=profit of $3
Black t-shirt=profit of $1.
To find the answer, selling price minus total money spent (shirt, printing) If the number is negative, it’s loss, and if it’s positive, it’s profit
A delivery person is carrying two packages. One package contains a 4-pound textbook and 5 identical workbooks. The other package contains a 6-pound textbook. The two packages weigh the same amount. What is the weight, in ounces, of each workbook? pls answer quick
write an equivalent expression for 2*14 / 2*2
Answer:
Step-by-step explanation:
if * means multiplication
the equivalent expression will be :
[tex]\frac{2.14}{2.2} = \frac{7}{7} = 7[/tex]
If the * means power :
then equivalent expression will be
[tex]\frac{2^{14} }{2^{2} } = 2^{(14-2)} =2^{12}[/tex]
[tex]\sqrt{x} 255\\[/tex]
The square root of 255 is approximately 15.969.
Given,
Root 255, [tex]\sqrt{255}[/tex]
We have to find the square root of the number:
Square root of a number:
A number multiplied by itself is the square root of that number. Or we may say that after adding a number to itself, we must calculate its square root in order to go back to the original number. The square root of p, if it is a positive integer, is represented by p, so that p = q.
Now,
√255 = 15.9687194227
Which is approximately equals to 15.969
That is,
The square root of 255 is approximately 15.969
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solve (3-4i) (6i+7) - (2-3i)
show solving steps-- picture is provided.
Answer:
-7 i + 43
Step-by-step explanation:
Simplify the following:
(-4 i + 3) (6 i + 7) - (-3 i + 2)
(3 - 4 i) (7 + 6 i) = 3×7 + 3×6 i - 4 i×7 - 4 i×6 i = 21 + 18 i - 28 i + 24 = 45 - 10 i:
(-10 i + 45) - (-3 i + 2)
-(-3 i + 2) = 3 i - 2:
45 - 10 i + (3 i - 2)
45 - 10 i - 2 + 3 i = (45 - 2) + (-10 i + 3 i) = 43 - 7 i:
Answer: -7 i + 43
Solve for "x"
4 (2x (2x - 1) - 1 (2x - 1)) = 0
Answer:
x = 1/2 or 0.5
Step-by-step explanation:
4 • ((2x • (2x - 1)) - (2x - 1)) = 0
The rule says: To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (2x-1) and the exponents are :
1, as (2x-1), is the same number as (2x-1)1
and 1, as (2x-1) is the same number as (2x-1)1
The product is therefore, (2x-1)(1+1) = (2x-1)2
4 • (2x - 1)2 = 0
4.2 Solve : (2x-1)2 = 0
(2x-1) 2 represents, in effect, a product of 2 terms which is equal to zero
For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means: 2x-1 = 0
Add 1 to both sides of the equation :
2x = 1
Divide both sides of the equation by 2:
x = 1/2 = 0.500
Answer:
x = 1/2.
Step-by-step explanation:
4 (2x (2x - 1) - 1 (2x - 1)) = 0
(2x (2x - 1) - 1 (2x - 1)) = 0
(2x - 1) is common to both parts.
(2x - 1)(2x - 1) = 0
2x - 1 = 0
x = 1/2.
a charity organization had to sell 18 tickets to their fundraiser just to cover necessary production costs. they sold each ticket for $45. let y represent the net profit (in dollars) when they have sold x tickets.
The equation which represents the net profit of the charity organization is y = 45x-810.
profit in math is described as the quantity gained from any commercial activity. due to the fact each ticket costs $45, the range of tickets bought ought to be accelerated by the fee of one ticket. because the question stated that x tickets had been sold, the amount could be $45 accelerated by x, which is $45x. To calculate the income, we ought to first calculate the cost of 18 tickets, which gives us the value charge, after which subtract it from the selling charge ($45x).The cost of 18 tickets is 18 x $45 = $810.profit = $45x-810y = 45x-810To learn more about profit, visit :
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the hawaii visitors bureau collects data on visitors to hawaii. the following questions were among 16 asked in a questionnaire handed out to passengers during incoming airline flights.
Using sampling concepts, the population being studied is all visitors that are flying to the state of Hawaii.
What is the missing information?The problem is incomplete, but researching it on a search engine, it asks for us to identify who is the population of this study.
What is population and sample?Population: Collection or set of individuals or objects or events whose properties will be studied.Sample: The sample is a subset of the population, and a well chosen sample, that is, a representative sample will contain most of the information about the population parameter. A representative sample means that all groups of the population are inserted into the sample.In this problem, a set of visitors traveling to Hawaii were sampled, hence the population being studied is all visitors that are flying to the state of Hawaii.
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This probability distribution shows the
typical distribution of pitches thrown to a
batter in a given "at-bat" in a baseball game.
Pitches
1
2 3 4 5
Frequency 15 20 40 15 10
Find the probability that the pitcher will
throw 4 or fewer pitches to a batter.
p = [?]
Enter
D
obtain expressions in component form for the position vectors having the following polar coordinates.
Expressions in component form for the position vectors having the polar coordinates are:
a) -12 cos(40)i + 12sin(40) j = -9.19i + 7.71j
b) 3cos(40) i + 3 sin(40) j = 2.29i + 1.92j
c) -24cos(48)i - 24sin(48) j = -16.059i - 17.83j
Polar coordinates can be found in :Use one or more of the following equations: cos=xr, sin=yr, tan=yx, and r=x2+y2 to convert rectangular coordinates to polar coordinates.
What exactly are polar coordinates?The polar coordinate system is indeed a two-dimensional coordinate system in which the distance from a reference point and the angle from a reference direction are used to determine each point's location on a plane. The polar axis is the ray emanating from the pole inside the reference direction. The pole is the point of reference.
According to the Given information:Let the +x and +y represent, respectively, the unit vectors represented by I and j.
(a) 12.6 m, 130° counterclockwise from the +x axis [tex]\overrightarrow{\mathrm{R}}[/tex]= m.
-12 cos(40)i + 12sin(40) j
= -9.19i + 7.71j
(b) 3.60 cm, 70.0° counterclockwise from the +x axis [tex]\overrightarrow{\mathrm{R}}[/tex]= cm.
3cos(40) i + 3 sin(40) j
= 2.29i + 1.92j
(c) 24.0 in., 206° counterclockwise from the +x axis [tex]\overrightarrow{\mathrm{R}}[/tex]= in.
-24cos(48)i - 24sin(48) j
= -16.059i - 17.83j
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I understand that the question you are looking for is:
Obtain expressions in component form for the position vectors having the following polar coordinates.
(a) 12.6 m, 130° counterclockwise from the +x axis
[tex]\overrightarrow{\mathrm{R}}[/tex]= m
(b) 3.60 cm, 70.0° counterclockwise from the +x axis
[tex]\overrightarrow{\mathrm{R}}[/tex]= cm
(c) 24.0 in., 206° counterclockwise from the +x axis
[tex]\overrightarrow{\mathrm{R}}[/tex]= in.
A submarine is only allowed to change its depth by rising toward the surface in 60-meter stages. It starts off at -340 meters.
At what depth is it after:
1 stage meters
2 stages meters
4 stages meters
How many full stages will it take to return to the surface?
Answer:
Can you only pick one answer?
Answers:
depth after 1 stage is -280 meters depth after 2 stages is -220 meters depth after 4 stages is -100 meters how many stages to return to the surface? 6 stages==========================================================
Explanation:
After 1 stage, the depth is -340+60*1 = -280 meters. In other words, it's 280 meters below the surface.
After 2 stages, the depth is now -340+60*2 = -220 meters
After 4 stages, the depth is -340+60*4 = -100 meters
After n stages, the depth is -340+60n. Set this equal to zero and solve for n.
-340+60n = 0
60n = 340
n = 340/60
n = 5.667 approximately
This rounds to n = 6
After n = 5 stages, the depth is -340+60n = -340+60*5 = -40 meters
After n = 6 stages, the depth is -340+60n = -340+60*6 = 20 meters, so the submarine is now at the surface. Of course the sub cannot fly to a height of 20 meters above the ocean's surface, so the highest it can go is 0 meters at the surface itself. This means the 6th stage is a movement of 40 meters (instead of 60 meters).
It might help to draw out a vertical number line to visually keep track of everything.
two soccer players are warming up by kicking soccer balls at a goalie. the two players are located 10 yards apart, and the angle from each player to the goalie is 64° and 75°, respectively. what is the distance from the farthest soccer player to the goalie?
Using the law of sines, it is found that the distance from the farthest soccer player to the goalie is 14.723 yards.
Given,
The distance between the two players = 10yards
The angle from each player to the goalie is 64° and 75°, respectively
We have to find,
the distance from the farthest soccer player to the goalie.
In this problem, considering that the sum of the internal angles of a triangle is of 180º, the angle that the goalie makes with the players is given by:
∠A = 180-(∠B+∠C)
∠A = 41°
Using Sine rule
AC/Sin B = BC / Sin A
AC = 10yrd*Sin75°/Sin41°
AC = 14.723 yards
The farthest distance is of 14.723 yards.
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q(x)=-2x-3
r(x)=-x+2
find the value of q(r(5))
Answer: q(r(5))= 3
Step-by-step explanation: sub in 5 for x in r(x). Once you do that, you'll get -3 for r(5). Now sub in the value of r(5), -3, for x in q(x). Then you'll end up with -9 once the equation has been evaluated.
1)
0.6
11
What would it be
Answer:as a fraction it would be 11 3/5
Step-by-step explanation:
question 7(multiple choice worth 1 points) (03.01 lc) what is the length of the unknown side of the right triangle? a right triangle with hypotenuse x and legs 5 and 12 13 17 25 60
The length of the unknown side of the right triangle is 13
What is a right angle triangle?A right triangle (American English), sometimes known as a right-angled triangle (British), is a triangle with one angle that is a right angle (i.e., a 90-degree angle), or two sides that are perpendicular. The link between is the basis of trigonometry.
between the right triangle's angles and sides.
The side across from the right angle is the hypotenuse (side c in the figure). Legs are the sides closest to the ideal angle (or catheti, singular: cathetus). The side a that is next to angle B and across from angle A is referred to as side b, and the side a that is next to angle A and across from angle B is referred to as side a.
Right triangles are referred to as Pythagorean triangles and their side lengths as Pythagorean if all three of their sides are integer lengths.
[tex]\sqrt{(12)^2+(5)^2}=13[/tex]
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